Babych scored the only goal in the relegation play-off game against Polissya Zhytomyr that allowed the Oleksandriya team to stay in the top tier.

He was then spotted by the Russian Premier League side Anzhi Makhachkala and was transferred to the club in 2003, playing there until 2005.

In February 2009, he moved to Chornomorets Odesa, where he was chosen captain on 15 July 2010, prior to the start of the 2010–11 season.

The subsequent two seasons of his career were, however, marred by injuries, and Babych had to retire as a player on 2 March 2012.

[2] At the beginning of July 2024 Babych became the head coach of the FC Chornomorets Odesa.